| Simple animals do not require the use of a brain to produce or synchronize the neurological impulses required for locomotion. The output from the non-brain neurological system of these simple animals stimulates muscle contractions that cause locomotion. The composite output of these neurological systems can be modeled using systems of coupled van der Pol oscillators.; Three different coupling topologies are presented where two are used to model the neural systems of the swimming lamprey and the jellyfish. Each system uses linear diffusive coupling between each pair of coupled oscillators as developed by Rand and Holmes [43].; This dissertation presents five new discoveries pertaining to the three different coupled systems: (1) a large order approximation of the solution and limit cycle solution of the van der Pol oscillator using the renormalization group method, (2) stability analysis for n coupled van der Pol oscillators where each oscillator is coupled to every oscillator, (3) numeric mapping of the in-phase transition curves of the three coupling topologies from three to six oscillators for non-linearity parameters (ϵ) of 1, 2.5 and 5, (4) numeric mapping of oscillatory modes of the three coupling topologies from three to six oscillators for ϵ = 1 and (5) application of the coupled van der Pol oscillators to modeling the composite output of the neural system of the jellyfish. |
